I'm sorry there is no easier way to update from an old image handler installation to the new one. Some files are not needed anymore and since the resizing went from admin side to the catalog side (on page request), some files in the admin section need to be replaced by their stock zen-cart equivalents.

The most generic way to update from a previous image handler installation would be as follows (I suppose):

Have a look at the old image handler zip. If you don't have it anymore, you should be able to retrieve the latest of the old 1.x releases on the breakmyzencart attic page. Replace every file on your server which matches the ones found inside the zip with it's stock zen-cart version. If there are no stock equivalents, delete them. (Pretty much a deinstallation). You shouldn't need to replace your template files as some functions have been added for backwards compatibility. Then go ahead and install the IH2 release.

I know, this is quite tedious and you might not need to replace all the files but as I said there is no easy way and I just can't know every possible problem that might surface since the possibilities of customizations are many. So apply the steps above with caution and backup your system before you start!

@Scott:There is just one additional icon which image handler needs, the other icons are modified to provide a more consistent look. All other binaries are needed. You can safely skip the duplicate icons and you can safely overwrite those icons, it's your choice. You should check your php files though, if they are already on your server. Image Handler 2 won't work if you miss a file provided in the zip, so you need to either overwrite or merge the matching php files. You can't just upload a part of it.

Kind regards,
Tim